Problem: Rewrite as a simplified fraction. ${0.1\overline{5} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 15.5555...\\ 10x &= 1.5555...\end{align*}}$ Subtracting the two equations, we have: ${90x = 14}$ ${x = \dfrac{14}{90}} $ ${x = \dfrac{7}{45}} $